Mathematics

Problem

Let for

x \in \mathbb{R}

f(x) = \frac{x + |x|}{2}

and

g(x) = \begin{cases} x, & x < 0 \\ x^2, & x \ge 0 \end{cases}

. Then area bounded by the curve

y = (f \circ g)(x)

and the lines

y = 0

2y - x = 15

is equal to _____. [JEE MAINS - ONLINE - 2023]